Wide-Sense Stationarity in Generalized Graph Signal Processing
arXiv:2112.01127 · doi:10.1109/TSP.2022.3184455
Abstract
We consider statistical graph signal processing (GSP) in a generalized framework where each vertex of a graph is associated with an element from a Hilbert space. This general model encompasses various signals such as the traditional scalar-valued graph signal, multichannel graph signal, and discrete- and continuous-time graph signals, allowing us to build a unified theory of graph random processes. We introduce the notion of joint wide-sense stationarity in this generalized GSP framework, which allows us to characterize a graph random process as a combination of uncorrelated oscillation modes across both the vertex and Hilbert space domains. We elucidate the relationship between the notions of wide-sense stationarity in different domains, and derive the Wiener filters for denoising and signal completion under this framework. Numerical experiments on both real and synthetic datasets demonstrate the utility of our generalized approach in achieving better estimation performance compared to traditional GSP or the time-vertex framework.
References in corpus (10)
- The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
- Discrete Signal Processing on Graphs
- Stationary signal processing on graphs
- Stationary Graph Processes and Spectral Estimation
- Graph signal processing for machine learning: A review and new perspectives
- Graph Frequency Analysis of Brain Signals
- Graph topology inference based on sparsifying transform learning
- A Hilbert Space Theory of Generalized Graph Signal Processing
- The linear conditional expectation in Hilbert space
- Integrals with values in Banach spaces and locally convex spaces